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circum.not[w83,jmc]	More: 1. Circumscribing when generalizing

	Consider at(Stanford, California) in view of the fact that,
although it is unlikely, the trustees could decide to move Stanford
to New Jersey.  In a sufficiently wide context, we might therefore
write  at(Stanford,California,s).  Our objectives are  the following:

1. We want to include  at(Stanford,California)  in a database without
even imagining that it might be movable.

2. We want to be able to generalize to wider contexts.  In these
such a generalization, it should be conceivable that Stanford is
movable.

3. When such a generalization is made, it is a non-monotonic conclusion,
that  at(Stanford,California)  is still the appropriate expression -
unless the movability of Stanford is considered.

4. Merely considering the possible movability of Stanford doesn't
prevent  at(Stanford,California) from being said.  However, we can
also say something like at(Stanford,California,s).

5. When we are forced to  at(Stanford,California,s),  the usual
properties of Stanford go along with it by suitable non-monotonic
reasoning.

6. The reasoning may force the splitting of the concept into
several.  Some refer to the University, which may move and some
refer to purely geographical features like Lake Lagunita which
continues immovable.  There is also the post office.

	In the above we have used  s  as a situation but perhaps
also as a context.  Pat Hayes and Bob Moore do things this way,
but I have always been dubious though without convincing objections.
We'll see whether we need distinct concepts.

	Here's a try at solving the problem:

	1. We reify at(Stanford,California)  so the alternate
formulations are now  holds(at(Stanford,California))  and
holds(at(Stanford,California),s).

at1(x,y) ≡ holds1(at(x,y))
holds1 p ≡ ∀s.belongs(s,s0*) ⊃ holds2(p,s)

Let us distinguish between contexts, denoted by  c,  and situations,
denoted by  s.  We have a relation of generalization between contexts,
c1 ≤ c2.

We have

holds(at(Stanford,California),c1)

c1 ≤ c2

holds(holds(at(Stanford,California),s0),c2)

constant(at(Stanford,California),c1)
variable(at(Stanford,California),c2)

Syntactic sugar:

1. There is a current context  cc,  and  p  stands for  holds(p,cc).

2. Perhaps the current context is considered to be outside all
contexts explicitly mentioned so far, but we can always make the
move of generalizing the context.  By itself this has no effect,
because for each proposition, we have the non-monotonic conjecture
that if it holds in a context, it holds in a wider context.

3. Perhaps  cc  can simply be regarded as an assumption, so each
p  is just  cc ⊃ p.  This doesn't work if we want to quantify over
contexts.

4. What would happen if we try to write

	in(s) ⊃ at(x,y)

instead of

	at(x,y,s)

and

	in(s) ⊃ holds(at(x,y))

instead of

	holds(at(x,y),s)?

These don't work, because in any model  at(x,y)  has to be true or
false.  So we would have

	(in(s) ⊃ ¬on(x,y)) ∧ (in(result(move(x,y),s)) ⊃ on(x,y))

1983 May 9

	Perhaps  at(Stanford, CA)  is to be interpreted not as
asserting that Stanford is in California but rather merely that
Stanford is in California is well supported.  We could then imagine
that  at(Stanford, CA)  is true, but certain unexpected events having
happened Stanford isn't ⊗really in California.

It seems better to reify  at(Stanford, CA) and have a suitable variety
of  holds  predicates.